feat(host): game-mode integration + dedicated game sessions

Implements design/gamemode-and-dedicated-sessions.md (Parts A1-A5 + B0-B2):
reconciles the merged display-management registry with session-mobile
Bazzite/SteamOS hosts and adds a per-launch dedicated gamescope mode.

- A1 DisplayOwnership {Owned,External,SessionManaged} + poolable_now(): the
  registry pools only what it owns, so gamescope managed/attach outputs are no
  longer double-owned by the registry AND the gamescope restore worker (fixes
  the game-mode-reconnect stale-node wedge).
- A2 validated reuse: (backend,mode,launch,epoch) reuse key + kept_display_alive
  liveness probe + reused_gen/mark_failed on a reused-display first-frame failure.
- A3 policy-driven managed restore (keep_alive replaces the hardcoded 5s debounce;
  forever = held = gaming-rig truthful) + crash-restore persist + SIGKILL teardown
  (kill_unit, applied to our transient unit AND the autologin stop -- validated
  live on .181 to avoid the F44 GPU-context leak).
- A4 session epoch: observe_session_instance bumps the epoch + invalidate_backend
  on a desktop-compositor instance change; gamescope spawns are exempt.
- A5 per-spawn log + PID-scoped gamescope node discovery.
- B0 game_session {auto,dedicated} policy (top-level, preset-orthogonal) +
  pick_gamescope_mode dedicated_launch + steam -silent command shaping.
- B1 free the autologin Steam before a dedicated Steam spawn (single-instance).
- B2 game-exit -> APP_EXITED_CLOSE_CODE (0x52) clean session end.

Adversarially reviewed (11 findings fixed). Validated on glass (.181 Bazzite F44,
RTX 4090): dedicated spawn streams a real game smoothly; keep-alive reuse; the
SIGKILL fix avoids the F44 vkCreateDevice leak. Workspace green
(build / test --workspace / clippy -D warnings / fmt), OpenAPI + C header
regenerated, web console tsc + vite build green. clients/probe: bump the
no-video timeout 8s->45s for gamescope cold starts.

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

include/punktfunk_core.h

@@ -283,6 +283,16 @@
 #define QUIT_CLOSE_CODE 81
 #endif
 
+#if defined(PUNKTFUNK_FEATURE_QUIC)
+// QUIC application error code the **host** closes the control connection with when a **dedicated game
+// session's game process exits** (the nested gamescope died — the user quit the game), so a launcher
+// client can distinguish "the game ended" from an error and return to its library cleanly rather than
+// surfacing a failure (`design/gamemode-and-dedicated-sessions.md` §5.3). Sibling of
+// [`QUIT_CLOSE_CODE`]; a client that doesn't special-case it still ends the session (every client
+// returns to its launcher on session end), so it is purely refinement. Shared so host + clients agree.
+#define APP_EXITED_CLOSE_CODE 82
+#endif
+
 #if defined(PUNKTFUNK_FEATURE_QUIC)
 // [`Hello::video_codecs`] bit: the client can decode H.264 / AVC. The GPU-less **software**
 // encode path (openh264) emits H.264, so a client that wants to stream from a software host MUST